Elements of Mechanical Engineering

Chapter 1. Introduction

Mitesh D. Gohil

Introduction:

• Prime movers and its types,

• System, Change of state, Path, Process, Cycle

• Concept of Force, Pressure, Energy, Work, Power

• Concept of, Heat, Temperature, Specific heat capacity,

Internal energy, Enthalpy,

• Statements of Zeroth Law and First law

Prime movers

• It is a device which uses the energy from natural sources and converts it into mechanical energy

Fig. Wind Mill

Fig. Solar Power Plant

(Central Tower Receiver type)

Up to 2000 °CFig. Heat Engine (IC)

Types of Prime Movers

Thermal

• Heat Engines

• Nuclear Power Plant

• Geothermal Power Plant

• Biogas Power Plant

• Solar Energy Power Plant

Non Thermal

• Hydraulic Turbines

Power Plants

• Tidal Power Plant

• Wind Mills

Que. What is Prime mover ? How prime movers are Classified ? GTU : June 2009, Jan 2011

Que. Define the following terms : Prime mover GTU : Dec 2010

Natural Energy Sources

Conventional or

Non-Renewable

• Wood

• Coal

• Coke

• Petrol

• Diesel

• Kerosene

• LPG

• CNG

• Methane

• Propane

• Nuclear

energy

(Unstable

U235, Th232)

Non Conventional or Renewable

• Hydraulic Power

• Geothermal

• Solar

• Bio gas and Bio mass

• Wind energy

• Tidal energy

• Wave energy

• Ocean thermal energy

Que. What are the various forms of energy ? List the non conventional sources of energy GTU : Dec 2008

Que. What do you mean by non-conventional energy sources ? How does it differ from conventional sources ?

GTU : Dec 2010

Thermodynamic System

• It is a fixed mass in region of space under consideration to analyze problem

System

System BoundarySurrounding

Real Imaginary

Universe = System + Surrounding

Que. Define the following terms : Boundary GTU : Nov-Dec 2010

Types of System

Fig. (a) Open System (b) Close System (c) Isolated System

Que. Classify thermodynamic system and give example of each. GTU : Dec 2011

Fig. a) Close System b) Open System with Control Volume

Open system CV :- The fixed volume in space of the open system under study is

called control volume and surface surrounding this volume is called control surface

Types of System

Que. Classify thermodynamic system and give example of each. GTU : Dec 2011

State of system

The Identification of the system by observable or measurable

quantities is called the state of the system

Important aspects of thermodynamic properties

• Distinguish one system form another

• Unique value of system

• Independent of the path followed by system

• Exact Differential, Example

1

2

𝑑𝑇 = 𝑇2 − 𝑇1

Properties :

It’s measurable quantity to describe the system which only depends on the

state of system and not on the path follow by system

Properties Types :

1. Intensive Properties :- Independent of the mass of the system

(Pressure (p), Temperature (T), Entropy (S), Enthalpy (H))

2. Extensive Properties :- Dependent of the mass of the system

(length (L), Volume (V), mass (M))

• Point Function

When two co-ordinates are located on the graph, They define a point and the two

properties on the graph define state. These properties (p, T, v) are called point function.

• Path Function

There are certain quantities like heat and work can not be located on a graph by a point

but there are represented by the area. It is not a state or point function, rather it depends

on the path of the process. Such quantities are called path function and they are inexact

differentials

Process

• If any one or more properties of the system undergo a change due to energy

or mass transfer we say that the system has undergone a change of state

• The successive change of state of the system due to energy or mass transfer

defined by definite path is called a process.

• The curve joining the successive state represents the process path

• If a system undergoes two or more processes and returns to its original state

after conclusion of processes, the system is said to have undergone a cycle

Thermodynamic equilibrium

• A system is said to be in thermodynamic equilibrium which is incapable of

any spontaneous change of its macroscopic properties (p, v, t) and it is in

complete balance with its surroundings.

• A system will be in thermodynamic equilibrium if it satisfies the condition

of mechanical, thermal and chemical equilibrium

Mechanical equilibrium :- No unbalance forces

Thermal Equilibrium :- Uniformity of temp. inside with surrounding

Chemical Equilibrium :- Absence of any chemical reaction

Quasi Static Process / Reversible• A quasi static process is defined as a process in which the properties of the system depart

infinitesimally (extremely small) from the thermodynamic equilibrium path

• If the properties of the system has finite departures from thermodynamic equilibrium path the

process is said to be non quasi static

• Quasi static process is the succession of thermodynamic equilibrium state while in case of non-

quasi static process the end states only represent the thermodynamic equilibrium.

• Condition for reversible process are

1. No Friction

2. Heat transfer is through infinitely temperature difference.

3. There are no spontaneous changes in the system.

• All processes in nature are irreversible.

Work done in moving boundary of close system in quasi-static process displacement work

• Force Exerted on piston, F = P A

• Small work done,

δw = F dlδw = P A dlδw = P dV

W = 12δw = 1

2P dV

• In non-quasi-static process, W ≠

12P dV because there is non unique value of ‘P’

• We conclude that the equation W = 12P dV is

valid for quasi-static & reversible process only.

dl

Weight

1

2

Gas

Piston area, A

Fig. Work of a quasi-equilibrium expansion

or compression process.

Fig. Illustration that work

depends on the process.

Work done in moving boundary of close system in quasi-static process displacement work

Homogeneous and Heterogeneous System

• If a system consist of homogeneous matter throughout in chemical composition and

physical Structure, it is called homogeneous system

• Example :- Ice, Water, Air, Vapor etc.

• While System Consisting of matter of different chemical compositions and/or

physical Structure is called heterogeneous system.

• Example :- Ice + Water, Two non miscible Liquid etc.

Homogeneous

System

Heterogeneous

System

Working Substance :- The fluid used in a thermodynamic system to serve as a

medium for transfer of energy between the system and its surrounding.

Pure Substance :- A pure substance is one which has a homogeneous and

invariable chemical composition even though there is a change of phase.

• Example:- liquid water, mixture of water and steam (Vapor), Mixture of ice

and water etc.

Fig. Pure Substance

Energy

• Energy can be defined as the capacity to do work

• Various form of energy

1) Internal

• Chemical Energy (chemical Bond)

• Atomic Energy (Atomic Structure of matter)

• Molecular Energy (Molecular motion and its configure)

2) External

• Potential Energy (P.E.) = m 𝑔 ℎ

• Kinetic Energy (K.E) = 1

2𝑚 𝑣2

Concept of Force

• Fundamental Physical Dimensions

1) Length L (m)

2) Mass M (kg)

3) Time T (s)

Force :- Newton’s Second law

Force is Directly Proportional to the rate of change of moment

𝐹 = 𝑑𝑑𝑡

𝑚 𝑣

𝐹 = 𝑚𝑎

Where,

F= Force (N)

m = mass (kg)

v = velocity (m/s)

a = Acceleration (m/𝑠2)

Pressure

It is the normal force exerted by a system per unit surface area

P = Pressure (Pa)

F = Force (N)

A = Area (𝑚2)

Weight

• Weight :- The weight of a body (W) is the force with which a body is attracted to the centre of earth.

W = m g (unit, N)

1 bar = 105 Pa1 atm = 1.01325 × 105 Pa

Que. Define Pressure. GTU : May 2013

P = 𝐹

𝐴

Pressure Measuring Devices

• Barometer

• Manometer

• Bourdon Pressure Gauge

Absolute Pressure

The pressure measured relatively to perfect vacuum is called absolute

pressure

Gauge Pressure

The pressure measured relatively to atmospheric pressure is called

gauge pressure

Que. Explain Absolute pressure, Gauge pressure and Atmospheric pressure. GTU : May 2013

Relationships among the absolute, atmospheric, gage, and vacuum pressures.

Absolute Pressure = Atmospheric Pressure + Gauge Pressure

Perfect Vacuum

Barometric Pressure :-

1.01325 × 105 = 𝜌𝑓× 9.8 × ℎ𝑓

• Water, 𝜌𝑤 = 1000 kg/𝑚3

• Height of water column, 𝐿𝑤= 10.33 m

• Mercury 𝜌𝑚 = 13 600 kg/𝑚3

• Height of mercury column, 𝐿𝑚= 0.76 m

• Atmospheric Pressure is defined as the pressure exerted by the atmosphere.

• Atmospheric pressure measured at Mean Sea Level (M.S.L) is equal to 1.01325 bar

Fig. Barometer

Patm = ρf g L

Manometer

Manometer is measuring device which measure the gauge pressure of fluid.

Absolute Pressure =

Atmospheric Pressure + Gauge Pressure

Liquid Used :- Mercury, oil etc.

Fig. Manometer

Pgauge(Tank) = ρf g L

Bourdon tube Pressure gauge

• Cross Sectional :- Elliptical

• The bent tube tends to unbend when

subjected to fluid pressure

• Deformation will transmitted from

bend tube to needle will show the

gauge pressure of the fluid on the

calibrated scale.

Fig. Bourdon tube Pressure gauge

Que. Explain with neat sketch Bourdon tube type pressure gauge GTU : June 2011

Phenomena Potential

Difference

Flow Quantity Resistant

Currant flow in Wire e.m.f. (V1−V2) Electric Current (I) Resistant (R)

Fluid Flow in Pipe Pressure

Difference

(P1−P2)

Discharge/ Volume

flow rate ( V)

Surface friction (f) and

Viscosity (µ)

Heat flow in bar Temperature

Difference

(T1−T2)

Heat Flow ( Q) 1

Thermal Conductivity (k)

Similarity of Different Quantities in Electrical and Mechanical System

Temperature

• The temperature is a property of the system or thermal state of a body

which distinguishes a hot body with a cold body

• Temperature of a body is proportional to stored molecular energy i.e.

the average molecular kinetic energy of the molecules in a system.

• Thermal Equilibrium means equality of temperature

• Measuring Device :- Thermometer

Que. Define the following terms : Temperature. GTU : Nov-Dec 2010

Temperature measuring Devices

Fig. Thermometers. (a) Liquid-in-glass. (b) Electrical-resistance (c) Infrared-sensing ear

thermometer.

Temperature Scale Relation Between (Celsius (C), Fahrenheit (F), Kelvin (K), Rankine (R))

• Fine relation between F & K

from equation (1) and (2)

• Kelvin is SI Unit of temperature

𝐅 = 𝟏. 𝟖𝐂 + 𝟑𝟐 …(1)

𝐊 = 𝐂 + 𝟐𝟕𝟑. 𝟏𝟓 …(2)

F = R – 459.67 …(3)

P -T plots of the experimental data

obtained from a constant-volume gas

thermometer using four different

gases at different (but low) pressures.

Temperature Scales

Concluded that

Absolute zero Temperature

= −273.15 ℃ = 0 K

Heat

• Heat is the form of energy which transfer without transfer of mass, from one body

to another body (or between system and surroundings) from higher temperature to

lower temperature by virtue of temperature difference between two bodies.

• Abbreviated as ‘Q’ and Unit is J (Joule)

• Heat Addition into system :- Positive ( +Q)

• Heat Rejection from system :- Negative (-Q)

• Extensive Property and Path Function (Inexact Differential)

𝑄 =

1

2

𝑄 𝑑𝑡

Sign Convention

Work

• Analogous to heat, work is also a transient form of energy which is observed when it crosses the boundaries of the system without transfer of mass

• It is Path Function

• Small work done due to displacement ds

𝛿𝑊 = 𝐹 ∙ 𝑑𝑠

• 𝑇𝑜𝑡𝑎𝑙 𝑊𝑜𝑟𝑘 𝐷𝑜𝑛𝑒, 𝑊 = 12𝐹 ∙ 𝑑𝑠

External and Internal Work

• System whose sole effect external to the system is to exert a force on

the surroundings. This work is called an external work.

• When the work done by the force of one part of the system (internal

force) on to another part of the same system, it is said that it has done

an internal work.

• We are only concerned with external work.

Work

Work done with displacement

• Work is a scalar quantity having the dimension of energy

W = F × d

• Power :- It is the time rate of doing work.

P=𝑑𝑤

𝑑𝑡=

𝑊

𝑡= 𝑊

Sign Convention:-

Work done by system +W

Work done on system –W

Heat addition in system +Q

Heat rejection from system -Q

+ Q

- Q

+ W

- W

System

surrounding

Fig. Sign Convention

𝑄 −𝑊 = ∆𝑈

Difference between heat and work

1. Heat can only transfer when there is difference of temperature

between the system and surrounding, while work transfer can take

place even without the change in temperature

2. In constant volume process though work can not take place, however

heat can be transferred.

3. In case of work transfer, its sole effect could be raising or lowering a

weight in the surrounding but in case of heat transfer other effects

are also observed.

Similarities between heat and work

1. Both heat and work exist in transit and these are never possessed or

contained in a system.

2. Both heat and work refer to boundary phenomena.

3. Both heat and work are path function and do not represent as the

properties of system (Inexact difference, 𝛿𝑥 )

Que. Write similarities between heat transfer and work transfer. GTU : June 2011

Specific heat of a substance.

• It is defined as the amount of heat required to raise the temperature of 1 kg of substance by 1 degree of temperature

C =Q

m (∆T)J/kg K

Q = heat transfer (J)

∆T = T2 − T2= temperature change

C = Specific heat, J/kg K

Que. Define Specific heat of a substance. GTU : Jan 2011

𝐐 = 𝐦 𝐂 (∆𝐓)

Specific heat of gas

1) Specific heat of gas at constant volume (CV)

It is the amount of heat required to raise the temperature of unit mass of gas

by one degree at constant volume.

2) Specific heat of gas at constant pressure (Cp)

It is the amount of heat required to raise the temperature of unit mass of gas

by one degree at constant pressure.

3) Adiabatic Index, γ or k

The ratio of specific heat at constant pressure to the specific heat at constant

volume is known as adiabatic index.

γ =Cp

CV

γ = 1.4 di-atomic gas

γ = 1.67 mono-atomic gas

Enthalpy

• It is total energy of the system

• Specific Enthalpy,

• U, p, V are point function, so H is point function and property of system

• Unit of Enthalpy (H) is kJ

• Unit of Specific Enthalpy (h) is kJ/kg

H = U + pV

h = u + pv

Zero law of thermodynamic

• If two bodies A and B are individually thermal equilibrium with a third body C

then the two bodies A and B will also be in thermal equilibrium with each other

A B

C

Que. State and explain zeroth law of thermodynamics. GTU : June 2009

Que. What is zeroth law of thermodynamics ? GTU : Dec 2011

Fig. Body A, B, C

Another word,TA = TC & TB= TC then TA = TB

First law of thermodynamic (Energy conservation law)

• “ Energy can neither be created nor-destroyed but it can be converted from one form to another.”

First law of thermodynamic applied to close System, Cyclic Process

If a close system goes through a cycle, the algebraic sum of total energy transfer to it as heat

and work is zero.

Close System

W

Q

Mass transfer = 0

𝑈1 𝑈1

State 1

Close System

Cyclic Process

State 1

𝛿𝑄 −𝛿𝑊 = 0

Que. State first law of thermodynamics. GTU : Dec 2008

Que. Define Following terms : First law of thermodynamics. GTU : Nov-Dec 2010

First law of thermodynamic applied to close System subjected to change of state (Process)

• If a closed system undergoes a change of state or process having both as heat and

work transfer as shown in fig., then the net energy transfer (Q - W) will be stored

by the system as internal energy ∆U

• If an infinitesimal process is carried out then,

∆𝐔 = 𝐔𝟏 − 𝐔𝟐

Close System

State 1-2Q −W = ∆U

Q W

Fig. Heat and work transfer during a process

δQ − δW = dU

Que. What is flow and non-flow process ? GTU : Dec 2011

Flow Process :- Processes carried out in open systems having mass flow across the boundaries are called flow process.Non-Flow Process :- While the processes carried out in closed system without mass transfer its boundaries are called Non-flow process.

Que. Barometer is used to measure ______( Ans. Pressure ) GTU : Dec 2012

Questions of GTU Exam

Example. An artificial satellite has a mass of 600 kg and is moving towards moon. Calculate its kinetic and potential energies in (MJ) relative to earth when it is 50 km from launching and moving at 2500 km/hr. Take acceleration of earth’s gravitational field as 790 cm/𝑠2

Nov 2010

Given Data :-m = 600 kg, g =7.9 m/𝑠2,h = 50 km = 50,000 m, v=2500 km/hr. = 694.44 m/s

1. Potential energy = m g h =2.37 × 108 J

2. Kinetic energy = 1

2𝑚𝑣2 = 1.44 × 108 J

1) Work J

2) Enthalpy J

3) Mean Effective Pressure Pa or N/𝑚2

4) Heat J

5) Power W or J/s

6) Force N

7) Energy J

8) Specific Heat J/kg K

9) Specific Volume 𝑚3/𝑘𝑔

10) Calorific value J/kg

11) Stroke m

12) Dryness Fraction Dimensionless

13) Efficiency Dimensionless

14) Swept Volume 𝑚3

Que. SI Units of Following GTU : Dec 2012

Thank You…